Chave presents an excellent algorithm and computer subprogram that evaluate Hankel transforms by quadrature and continued fraction summation. This subprogram would be a valuable addition to any mathematical computer library. Chave refers to digital filter (convolution) methods as “the standard numerical approach to the computation of Hankel transforms,” and makes numerous references to my publi...

We elaborate on a correspondence between the coefficients of a multivariate polynomial represented in the Bernstein basis and in a tensor-monomial basis, which leads to homography representations of polynomial functions, that use only integer arithmetic (in contrast to Bernstein basis) and are feasible over unbounded regions. Then, we study an algorithm to split this representation and we obtai...

In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are based on the Euclidean algorithm and are of quadratic complexity.

We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.